If the Milky Way and the Andromeda galaxies are approximately 2 million light years apart and are moving toward each other at 199 km/sec, how long will it take before the two galaxies collide?
To determine the time it takes for the Milky Way and Andromeda galaxies to collide, we can use the formula:
Time = Distance / Relative Velocity
1. First, we need to convert the given relative velocity from km/s to light years per year.
Since 1 light year is approximately 9.461 × 10^12 km, we can calculate the relative velocity in light years per year as:
Relative Velocity = 199 km/s * (1 year/31,536,000 seconds) * (1 light year/9.461 × 10^12 km)
2. Next, we will calculate the time it takes for the galaxies to collide by dividing the distance between them by the relative velocity.
Time = 2,000,000 light years / Relative Velocity
Let's perform the calculations:
Relative Velocity = 199 km/s * (1 year/31,536,000 seconds) * (1 light year/9.461 × 10^12 km)
= 6.28 x 10^-5 light years/year
Time = 2,000,000 light years / Relative Velocity
= 2,000,000 light years / (6.28 x 10^-5 light years/year)
= 3.18 x 10^9 years
Therefore, it will take approximately 3.18 billion years for the Milky Way and Andromeda galaxies to collide.